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Geometrical Optics question

2025 · 22 Jan · Shift 2 · Q60
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Geometrical Optics question

2025 · 22 Jan · Shift 2 · Q60

JEE MainPhysicsGeometrical OpticsMCQ+4 / −1
A symmetric thin biconvex lens is cut into four equal parts by two planes ABA BAB and CDC DCD as shown in figure. If the power of original lens is 4D then the power of a part of the divided lens is JEE Main 2025 (Online) 22nd January Evening Shift Physics - Geometrical Optics Question 31 English
  1. A
    2D
  2. B
    8D
  3. C
    4D
  4. D
    D
View written solutionFree

Correct answer: C: 4D

  1. Power of a thin lens

For a thin lens in air, P=(μ−1)(1R1−1R2)P = (\mu-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)P=(μ−1)(R1​1​−R2​1​) where PPP is the power.

For a symmetric biconvex lens,

  • R1=+RR_1 = +RR1​=+R
  • R2=−RR_2 = -RR2​=−R

So,

= (\mu-1)\left(\frac{2}{R}\right)$$ Given original power, $$P=4\,\text{D}$$ --- 2. **Effect of cutting the lens** The lens is cut into four equal parts by two planes as shown. Such cutting changes the **aperture/size** of each part, but does not change the radii of curvature of the refracting surfaces for each piece. Hence, the focal length and therefore the **power of each part remain unchanged**. So each part has the same power as the original lens: $$P' = 4\,\text{D}$$ --- 3. **Check the options** - A: $2\,\text{D}$ ❌ - B: $8\,\text{D}$ ❌ - C: $4\,\text{D}$ ✅ - D: $1\,\text{D}$ ❌ Thus, the correct option is: $$\boxed{4\,\text{D}}$$ --- 4. **Comparison with stored answer** Stored correct answer: **A = $2\,\text{D}$** My derived answer is **C = $4\,\text{D}$**. The stored answer appears incorrect, because cutting a thin lens into pieces by planes containing/parallel to the principal axis changes only the aperture, not the curvatures, so the power of each piece remains the same as the original lens.
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